MSE2020LectureNotes_4_12

MSE2020LectureNotes_4_12 - M SE 2020 4/12/2011 Page 1 of 3...

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Unformatted text preview: M SE 2020 4/12/2011 Page 1 of 3 Lo ren tz Facto r (con t.) • Another 1sin2θB d ue to location of detector, so Lorentz factor∝cosθBsin22θB=14sin2θBcosθB • Polarization factor o Comes from oscillation of electron cloud, due to x-rays, which can scatter t he light o • LP Factor= 1+cos2θB8sin2θBcosθB∝1+cos2θBsin2θBcosθB o • Polarization factor= 1+cos2θB2 Shows θ dependence Overall decrease as θ i ncreases due to L-P factor o St r uct u re Facto r • • x<d • B = random point along h00 axis • δ1'2'=NC+CM=2dsinθ=λ M SE 2020 4/12/2011 Page 2 of 3 • Assum ing that it’s a cubic system, dh00=ah2+02+02=ah • ΔARB and ΔAMC are sim ilar • ΔASB and ΔANC are also sim ilar o • RBMC=ABAC=BSCN δ3'1'=RB+BS=MCABAC+CNABAC=ABACMC+CN=ABAC2dsinθ=ABACλ=λ xd=λhxa o Phase shift : φ=2πδλ o Phase difference between random ray scat tering and scat tering off real p lane: φ3'1'=δ3'1'*2πλ=2πhxa=2πhu o u=xa • Extend to 2 other dimensions • 3D Case: v=yb, w=zc o φ=2π(hu+kv+lw) • Elect ron wave has form: Aeiφ=fe2π(hu+kv+lw) • St ructure factor: F=1nfne2π(hu+kv+lw) o o • Amount of scattering (amplit ude = f n ) Gives information about basis Unit cell w/1 atom at origin o o Scattering intensity∝F2=f2 o • F=fe2πi(0*u+0*v+0*w)=fe0=f No weird interferences Base center unit cell o F=fe2πi(0)+fe2π(h+k2)=f(1+eπi(h+k) o If h+k is even, 2π rotation M SE 2020 4/12/2011 o Page 3 of 3 Unmixed: F=f1+1=2f→I=F2=4f2 If h+k is odd, π rotation No peak – absent peak o Mixed: F=f1-1=0→I=0 This means that certain planes will not show up in graph ...
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MSE2020LectureNotes_4_12 - M SE 2020 4/12/2011 Page 1 of 3...

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